The equation 2j = k - 5m relates the distinct positive integers j, k, and m. Which equation correctly expresses...

1. TRANSLATE the problem requirement

• Given: \(\mathrm{2j = k - 5m}\)
• Goal: Express j in terms of k and m (solve for j)

2. INFER the solution strategy

• Since j is multiplied by 2, we need to divide both sides by 2 to isolate j
• This will give us j by itself on the left side

3. SIMPLIFY by applying the division

• Divide both sides by 2:
  \(\mathrm{2j \div 2 = (k - 5m) \div 2}\)
• The left side simplifies to \(\mathrm{j}\)
• The right side becomes \(\mathrm{(k - 5m)/2}\)
• Result: \(\mathrm{j = (k - 5m)/2}\)

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students incorrectly distribute the division, dividing only the first term on the right side.

They might think: "Divide both sides by 2" means \(\mathrm{j = k/2 - 5m}\), forgetting that the entire expression \(\mathrm{(k - 5m)}\) must be divided by 2 as a unit.

This leads them to select Choice A (\(\mathrm{j = k/2 - 5m}\))

Second Most Common Error:

Poor understanding of order of operations: Students misinterpret which part gets divided by 2.

They might think the division only applies to the 5m term, getting \(\mathrm{j = k - 5m/2}\), rather than understanding that parentheses are needed to show \(\mathrm{(k - 5m) \div 2}\).

This leads them to select Choice B (\(\mathrm{j = k - 5m/2}\))

The Bottom Line:

This problem tests whether students understand that when solving equations, operations must be applied to entire expressions, not just individual terms. The key insight is recognizing that \(\mathrm{(k - 5m)}\) acts as a single unit when divided by 2.